Lake ecosystems: A polyhedral dynamics representation

Abstract For water quality problems involving global changes in the structure of the aquatic ecosystem, differential equation representations are often inadequate. A technique for modeling the global structure and dynamic behavior of such systems, called polyhedral dynamics, is presented by means of a simple yet realistic example. The lake ecosystem, composed of organic and inorganic nutrients, light, phytoplankton, zooplankton and fish, is represented as a multidimensional “graph” using a technique labeled “Q-analysis”, then a flow pattern is superimposed upon the “Q-analysis” to describe the dynamic behavior of the system. The importance of each element may be measured by its connectivity level with the other elements of the system. In this way, a strong correlation is found between the results obtained through Q-analysis and traditional ecological thinking. In other words, a Q-analysis can be used to gain insight into a complex process such as lake eutrophication. Also, consideration of the dynamic behavior gives a quantitative basis to the qualitative changes which an ecosystem undergoes as a result of increased nutrient loading. The approach may thus be used to assess the effectiveness of alternative eutrophication control methods.